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A Parameterized Complexity Tutorial

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Language and Automata Theory and Applications (LATA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7183))

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Abstract

The article was prepared for the LATA 2012 conference where I will be presenting two one and half hour lectures for a short tutorial on parameterized complexity. Much fuller accounts can be found in the books Downey-Fellows [33, 34], Niedermeier [72], Flum-Grohe [49], the two issues of the Computer Journal [36] and the recent survey Downey-Thilikos [39].

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References

  1. Abrahamson, K., Downey, R., Fellows, M.: Fixed-Parameter Intractability II. In: Enjalbert, P., Wagner, K.W., Finkel, A. (eds.) STACS 1993. LNCS, vol. 665, pp. 374–385. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  2. Abrahamson, K., Downey, R., Fellows, M.: Fixed-parameter tractability and completeness IV: On completeness for W[P] and PSPACE analogs. Annals of Pure and Applied Logic 73, 235–276 (1995), http://www.mrfellows.net/papers/J31-fpt4-95.pdf

    Article  MathSciNet  MATH  Google Scholar 

  3. Abu-Khzam, F.N., Fellows, M., Langston, M.A., Suters, W.H.: Crown structures for vertex cover kernelization. Theory Comput. Syst. 41(3), 411–430 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Abu-Khzam, F.N., Langston, M.A., Shanbhag, P., Symons, C.T.: Scalable parallel algorithms for FPT problems. Algorithmica 45(3), 269–284 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Adler, I., Grohe, M., Kreutzer, S.: Computing excluded minors. In: Proceedings of the of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2008, pp. 641–650. SIAM (2008)

    Google Scholar 

  6. Alekhnovich, M., Razborov, A.A.: Resolution is not automatizable unless W[P] is tractable. In: FOCS, pp. 210–219. IEEE Computer Society (2001)

    Google Scholar 

  7. Alon, N., Yuster, R., Zwick, U.: Color-coding: a new method for finding simple paths, cycles and other small subgraphs within large graphs. In: Proc. Symp. Theory of Computing (STOC), pp. 326–335. ACM (1994)

    Google Scholar 

  8. Bazgan, C.: Schémas d’approximation et complexité paramétrée, Rapport de stage de DEA d’Informatique à Orsay. Tech. rep., Informatique d’Orsay (1995)

    Google Scholar 

  9. Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing 25, 1305–1317 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bodlaender, H.L., Downey, R., Fellows, M., Hallett, M.T., Wareham, H.T.: Parameterized complexity analysis in computational biology. Computer Applications in the Biosciences 11, 49–57 (1995)

    Google Scholar 

  11. Bodlaender, H.L., Downey, R., Fellows, M., Hermelin, D.: On problems without polynomial kernels. Journal of Computing and System Sciences 75(8), 423–434 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bodlaender, H.L., Fomin, F.V., Lokshtanov, D., Penninkx, E., Saurabh, S., Thilikos, D.M.: (Meta) kernelization. In: FOCS, pp. 629–638. IEEE Computer Society (2009)

    Google Scholar 

  13. Bodlaender, H.L., Koster, A.M.C.A.: Combinatorial optimization on graphs of bounded treewidth. The Computer Journal 51, 255–269 (2008)

    Article  Google Scholar 

  14. Bodlaender, H.L., Thomasse, S., Yeo, A.: Analysis of data reduction, transformations give evidence for non-existence of polynomial kernels. Tech. Rep. UU-CS-2008-030, Utrecht University (2008)

    Google Scholar 

  15. Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters 58(4), 171–176 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  16. Cai, L., Chen, J., Downey, R., Fellows, M.: On the parameterized complexity of short computation and factorization. Arch. for Math. Logic 36, 321–337 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. Cai, L., Fellows, M., Juedes, D.W., Rosamond, F.A.: The complexity of polynomial-time approximation. Theoretical Computer Science 41, 459–477 (2007)

    MathSciNet  MATH  Google Scholar 

  18. Cai, L., Juedes, D.W.: Subexponential Parameterized Algorithms Collapse the W-Hierarchy. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 273–284. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Cai, L., Juedes, D.W.: On the existence of subexponential parameterized algorithms. Journal of Computing and Systems Science 67, 789–807 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Cheetham, J., Dehne, F.K.H.A., Rau-Chaplin, A., Stege, U., Taillon, P.J.: Solving large FPT problems on coarse-grained parallel machines. Journal of Computer and Systems Sciences 67(4), 691–706 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen, J., Chor, B., Fellows, M., Huang, X., Juedes, D.W., Kanj, I.A., Xia, G.: Tight lower bounds for certain parameterized NP-hard problems. Information and Computation 201, 216–231 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Chen, J., Kanj, I.A., Xia, G.: Improved upper bounds for vertex cover. Theor. Comput. Sci. 411, 3736–3756 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Chen, Y., Flum, J., Müller, M.: Lower bounds for kernelizations and other preprocessing procedures. Theory Comput. Syst. 48(4), 803–839 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Courcelle, B.: Recognizability and second-order definability for sets of finite graphs. Tech. Rep. I-8634, Universite de Bordeaux (1987)

    Google Scholar 

  25. Demaine, E.D., Hajiaghayi, M.: The bidimensionality theory and its algorithmic applications. Comput. J. 51(3), 292–302 (2008)

    Article  Google Scholar 

  26. Downey, R.: Parameterized complexity for the skeptic. In: Proc. 18th IEEE Annual Conference on Computational Complexity, pp. 147–169 (2003)

    Google Scholar 

  27. Downey, R., Fellows, M.: Fixed parameter tractability and completeness. In: Ambos-Spies, K., Homer, S., Schöning, U. (eds.) Complexity Theory: Current Research, pp. 161–187. Cambridge University Press (1992); congressus Numerantium, 87

    Google Scholar 

  28. Downey, R., Fellows, M.: Fixed-parameter intractability. In: Structure in Complexity Theory Conference, pp. 36–49 (1992)

    Google Scholar 

  29. Downey, R., Fellows, M.: Fixed-parameter tractability and completeness III: Some structural aspects of the W-hierarchy. In: Ambos-Spies, K., Homer, S., Schöning, U. (eds.) Complexity Theory: Current Research - Proceedings of the 1992 Dagstuhl Workshop on Structural Complexity, pp. 166–191. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  30. Downey, R., Fellows, M.: Fixed-parameter tractability and completeness I: Basic theory. SIAM Journal of Computing 24, 873–921 (1995), http://mrfellows.net/papers/J29-completeness1-95.ps

    Article  MATH  Google Scholar 

  31. Downey, R., Fellows, M.: Fixed-parameter tractability and completeness II: Completeness for W[1]. Theoretical Computer Science A 141, 109–131 (1995), http://mrfellows.net/papers/J30-CompletenessII-95.ps

    Article  MathSciNet  MATH  Google Scholar 

  32. Downey, R., Fellows, M.: Parameterized computational feasibility. In: Clote, P., Remmel, J. (eds.) Proceedings of the Second Cornell Workshop on Feasible Mathematics. Feasible Mathematics II, pp. 219–244. Birkhäuser, Boston (1995), http://mrfellows.net/papers/C17-feasibility95.ps

  33. Downey, R., Fellows, M.: Parameterized Complexity, 530 pages. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  34. Downey, R., Fellows, M.: Fundamentals of Parameterized Complexity. Springer, Heidelberg (in preparation, 2012)

    Google Scholar 

  35. Downey, R., Fellows, M., Kapron, B., Hallett, M., Wareham, H.T.: The Parameterized Complexity of Some Problems in Logic and Linguistics. In: Matiyasevich, Y.V., Nerode, A. (eds.) LFCS 1994. LNCS, vol. 813, pp. 89–100. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  36. Downey, R., Fellows, M., Langston, M.: Two Special Issue of The Computer Journal Special Issue on Parameterized Complexity. The Computer Journal 51(1 and 3) (2008), http://mrfellows.net/papers/J71-Jforward08.pdf

  37. Downey, R., Fellows, M., McCartin, C., Rosamond, F.: Parameterized approximation of dominating set problems. Information Processing Letters 109(1), 68–70 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  38. Downey, R., Fellows, M., Regan, K.W.: Parameterized circuit complexity and the W hierarchy. Theoretical Computer Science A 191(1-2), 97–115 (1998), http://mrfellows.net/papers/DFR98_CircuitComplexity.pdf

    Article  MathSciNet  MATH  Google Scholar 

  39. Downey, R., Thilikos, D.M.: Confronting intractability via parameters. Computer Science Review 5, 279–317 (2011)

    Article  MATH  Google Scholar 

  40. Edmonds, J.: Paths, trees, and flowers. Canad. J. Math. 17, 449–467 (1965), http://www.cs.berkeley.edu/~christos/classics/edmonds.ps

    Article  MathSciNet  MATH  Google Scholar 

  41. Eickmeyer, K., Grohe, M., Grüber, M.: Approximation of natural W[P]-Complete minimisation problems is hard. In: Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity, CCC 2008, pp. 8–18. IEEE Computer Society, Washington, DC (2008), http://dx.doi.org/10.1109/CCC.2008.24

    Chapter  Google Scholar 

  42. Fellows, M., Langston, M.A.: Nonconstructive advances in polynomial-time complexity. Information Processing Letters 26(3), 155–162 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  43. Fellows, M., Langston, M.A.: Nonconstructive tools for proving polynomial-time decidability. Journal of the Association for Computing Machinery 35(3), 727–739 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  44. Fellows, M., Langston, M.A.: An analogue of the Myhill-Nerode theorem and its use in computing finite-basis characterizations. In: Proceedings of the IEEE Symposium on the Foundations of Computer Science (FOCS), pp. 520–525. IEEE Computer Society (1989)

    Google Scholar 

  45. de Fluiter, B.: Algorithms for graphs of small treewidth. Ph.D. thesis, Utrecht University (1970)

    Google Scholar 

  46. Flum, J., Grohe, M.: Describing Parameterized Complexity Classes. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 359–371. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  47. Flum, J., Grohe, M.: The parameterized complexity of counting problems. In: Proceedings of the 43rd IEEE Symposium on Foundations of Computer Science (FOCS 2002), pp. 538–547. IEEE Computer Society (2002)

    Google Scholar 

  48. Flum, J., Grohe, M.: Parametrized complexity and subexponential time. Bulletin of the EATCS 84, 71–100 (2004)

    MATH  Google Scholar 

  49. Flum, J., Grohe, M.: Parameterized complexity theory. Texts in theoretical computer science. Springer, Heidelberg (2006), http://books.google.com/books?id=VfJz6hvFAjoC

    MATH  Google Scholar 

  50. Fortnow, L., Santhanam, R.: Infeasibility of instance compression and succinct PCPs for NP. Journal of Computing and System Sciences 77(1), 91–106 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  51. Frick, M., Grohe, M.: Deciding first-order properties of locally tree-decomposable structures. J. ACM 48(6), 1184–1206 (2001), http://doi.acm.org/10.1145/504794.504798

    Article  MathSciNet  MATH  Google Scholar 

  52. Frick, M., Grohe, M.: The complexity of first-order and monadic second-order logic revisited. In: Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science, LICS 2002, pp. 215–224. IEEE Computer Society, Washington, DC (2002)

    Google Scholar 

  53. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  54. Goldberg, P.W., Golumbic, M.C., Kaplan, H., Shamir, R.: Four strikes against physical mapping of DNA. Journal of Computational Biology 2(1), 139–152 (1993)

    Article  Google Scholar 

  55. Gramm, J., Niedermeier, R., Rossmanith, P.: Exact Solutions for Closest String and Related Problems. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 441–453. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  56. Grohe, M.: Generalized Model-Checking Problems for First-Order Logic. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 12–26. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  57. Grohe, M., Kreutzer, S.: Methods for algorithmic meta theorems. In: Grohe, M., Makowsky, J. (eds.) Model Theoretic Methods in Finite Combinatorics. Contemporary Mathematics, vol. 558. American Mathematical Society (2011)

    Google Scholar 

  58. Hallett, M., Mccartin, C.: A faster FPT algorithm for the maximum agreement forest problem. Theory of Computing Systems 41(3), 539–550 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  59. Hermelin, D., Kratsch, S., Soltys, K., Whalstrom, M., Wu, X.: Hierarchies of inefficient kernelization (to appear)

    Google Scholar 

  60. Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? Journal of Computer and System Sciences 63(4), 512–530 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  61. Karp, R.: Reducibility among combinatorial problems. In: Miller, R., Thatcher, J. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)

    Google Scholar 

  62. Karp, R.: Heuristic algorithms in computational molecular biology. Journal of Computer and System Sciences 77(1), 122–128 (2011), http://dx.doi.org/10.1016/j.jcss.2010.06.009

    Article  MathSciNet  MATH  Google Scholar 

  63. Khot, S., Raman, V.: Parameterized complexity of finding subgraphs with hereditary properties. Theoretical Computer Science 289(2), 997–1008 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  64. Langston, M.A., Perkins, A.D., Saxton, A.M., Scharff, J.A., Voy, B.H.: Innovative computational methods for transcriptomic data analysis: A case study in the use of FPT for practical algorithm design and implementation. The Computer Journal 51(1), 26–38 (2008)

    Article  Google Scholar 

  65. Mahajan, M., Raman, V.: Parameterizing above guaranteed values: MaxSat and MaxCut. Journal Algorithms 31(2), 335–354 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  66. Marx, D.: Future directions in parameterized complexity (tentative title) (to appear, 2012)

    Google Scholar 

  67. McCartin, C.: Parameterized counting problems. Annals of Pure and Applied Logic 138(1-3), 147–182 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  68. Müller, M.: Randomized Approximations of Parameterized Counting Problems. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 50–59. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  69. Müller, M.: Valiant-Vazirani Lemmata for various logics. Electronic Colloquium on Computational Complexity (ECCC) 15(063) (2008)

    Google Scholar 

  70. Nemhauser, G., Trotter Jr., L.: Vertex packings: Structural properties and algorithms. Mathematical Programming 8, 232–248 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  71. Niedermeier, R.: Invitation to fixed-parameter algorithms. Habilitationschrift, University of Tübingen (2002)

    Google Scholar 

  72. Niedermeier, R.: Invitation to fixed-parameter algorithms. Oxford lecture series in mathematics and its applications. Oxford University Press (2006), http://books.google.com/books?id=mAA_OkeJxhsC

  73. Niedermeier, R., Rossmanith, P.: A general method to speed up fixed-parameter-tractable algorithms. Information Processing Letters 73, 125–129 (2000), http://theinf1.informatik.uni-jena.de/publications/ipl00.pdf

    Article  MathSciNet  MATH  Google Scholar 

  74. Papadimitriou, C.H., Yannakakis, M.: On the complexity of database queries. In: PODS, pp. 12–19. ACM Press (1997); Journal Version in Journal of Computer System Sciences 58, 407–427 (1999)

    Google Scholar 

  75. Reed, B., Smith, K., Vetta, A.: Finding odd cycle transversals. Operations Research Letters 32(4), 299–301 (2004), http://dx.doi.org/10.1016/j.orl.2003.10.009

    Article  MathSciNet  MATH  Google Scholar 

  76. Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms 7(3), 309–322 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  77. Weerapurage, D.P., Eblen, J.D., Rogers, G., Langston, M.A.: Parallel Vertex Cover: A Case Study in Dynamic Load Balancing. In: Chen, J., Ranjan, R. (eds.) Australasian Symposium on Parallel and Distributed Computing (AusPDC 2011). CRPIT, vol. 118, pp. 25–32. ACS, Perth (2011), http://crpit.com/confpapers/CRPITV118Weerapurage.pdf

    Google Scholar 

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  1. School of Mathematics, Statistics and Operations Research, Victoria University, P.O. Box 600, Wellington, New Zealand

    Rod Downey

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  1. Rod Downey
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  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

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Downey, R. (2012). A Parameterized Complexity Tutorial. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_4

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